Chris Moreh, 2023
Week 2
Revisiting Flatland
A review of general linear models
[1] 151.7650 139.7000 136.5250 156.8450 145.4150 163.8300 149.2250 168.9100
[9] 147.9550 165.1000 154.3050 151.1300 144.7800 149.9000 150.4950 163.1950
[17] 157.4800 143.9418 121.9200 105.4100 86.3600 161.2900 156.2100 129.5400
[25] 109.2200 146.4000 148.5900 147.3200 137.1600 125.7300 114.3000 147.9550
[33] 161.9250 146.0500 146.0500 152.7048 142.8750 142.8750 147.9550 160.6550
[41] 151.7650 162.8648 171.4500 147.3200 147.9550 144.7800 121.9200 128.9050
[49] 97.7900 154.3050 143.5100 146.7000 157.4800 127.0000 110.4900 97.7900
[57] 165.7350 152.4000 141.6050 158.8000 155.5750 164.4650 151.7650 161.2900
[65] 154.3050 145.4150 145.4150 152.4000 163.8300 144.1450 129.5400 129.5400
[73] 153.6700 142.8750 146.0500 167.0050 158.4198 91.4400 165.7350 149.8600
[81] 147.9550 137.7950 154.9400 160.9598 161.9250 147.9550 113.6650 159.3850
[89] 148.5900 136.5250 158.1150 144.7800 156.8450 179.0700 118.7450 170.1800
[97] 146.0500 147.3200 113.0300 162.5600 133.9850 152.4000 160.0200 149.8600
[105] 142.8750 167.0050 159.3850 154.9400 148.5900 111.1250 111.7600 162.5600
[113] 152.4000 124.4600 111.7600 86.3600 170.1800 146.0500 159.3850 151.1300
[121] 160.6550 169.5450 158.7500 74.2950 149.8600 153.0350 96.5200 161.9250
[129] 162.5600 149.2250 116.8400 100.0760 163.1950 161.9250 145.4150 163.1950
[137] 151.1300 150.4950 141.6050 170.8150 91.4400 157.4800 152.4000 149.2250
[145] 129.5400 147.3200 145.4150 121.9200 113.6650 157.4800 154.3050 120.6500
[153] 115.6000 167.0050 142.8750 152.4000 96.5200 160.0000 159.3850 149.8600
[161] 160.6550 160.6550 149.2250 125.0950 140.9700 154.9400 141.6050 160.0200
[169] 150.1648 155.5750 103.5050 94.6150 156.2100 153.0350 167.0050 149.8600
[177] 147.9550 159.3850 161.9250 155.5750 159.3850 146.6850 172.7200 166.3700
[185] 141.6050 142.8750 133.3500 127.6350 119.3800 151.7650 156.8450 148.5900
[193] 157.4800 149.8600 147.9550 102.2350 153.0350 160.6550 149.2250 114.3000
[201] 100.9650 138.4300 91.4400 162.5600 149.2250 158.7500 149.8600 158.1150
[209] 156.2100 148.5900 143.5100 154.3050 131.4450 157.4800 157.4800 154.3050
[217] 107.9500 168.2750 145.4150 147.9550 100.9650 113.0300 149.2250 154.9400
[225] 162.5600 156.8450 123.1900 161.0106 144.7800 143.5100 149.2250 110.4900
[233] 149.8600 165.7350 144.1450 157.4800 154.3050 163.8300 156.2100 153.6700
[241] 134.6200 144.1450 114.3000 162.5600 146.0500 120.6500 154.9400 144.7800
[249] 106.6800 146.6850 152.4000 163.8300 165.7350 156.2100 152.4000 140.3350
[257] 158.1150 163.1950 151.1300 171.1198 149.8600 163.8300 141.6050 93.9800
[265] 149.2250 105.4100 146.0500 161.2900 162.5600 145.4150 145.4150 170.8150
[273] 127.0000 159.3850 159.4000 153.6700 160.0200 150.4950 149.2250 127.0000
[281] 142.8750 142.1130 147.3200 162.5600 164.4650 160.0200 153.6700 167.0050
[289] 151.1300 147.9550 125.3998 111.1250 153.0350 139.0650 152.4000 154.9400
[297] 147.9550 143.5100 117.9830 144.1450 92.7100 147.9550 155.5750 150.4950
[305] 155.5750 154.3050 130.6068 101.6000 157.4800 168.9100 150.4950 111.7600
[313] 160.0200 167.6400 144.1450 145.4150 160.0200 147.3200 164.4650 153.0350
[321] 149.2250 160.0200 149.2250 85.0900 84.4550 59.6138 92.7100 111.1250
[329] 90.8050 153.6700 99.6950 62.4840 81.9150 96.5200 80.0100 150.4950
[337] 151.7650 140.6398 88.2650 158.1150 149.2250 151.7650 154.9400 123.8250
[345] 104.1400 161.2900 148.5900 97.1550 93.3450 160.6550 157.4800 167.0050
[353] 157.4800 91.4400 60.4520 137.1600 152.4000 152.4000 81.2800 109.2200
[361] 71.1200 89.2048 67.3100 85.0900 69.8500 161.9250 152.4000 88.9000
[369] 90.1700 71.7550 83.8200 159.3850 142.2400 142.2400 168.9100 123.1900
[377] 74.9300 74.2950 90.8050 160.0200 67.9450 135.8900 158.1150 85.0900
[385] 93.3450 152.4000 155.5750 154.3050 156.8450 120.0150 114.3000 83.8200
[393] 156.2100 137.1600 114.3000 93.9800 168.2750 147.9550 139.7000 157.4800
[401] 76.2000 66.0400 160.7000 114.3000 146.0500 161.2900 69.8500 133.9850
[409] 67.9450 150.4950 163.1950 148.5900 148.5900 161.9250 153.6700 68.5800
[417] 151.1300 163.8300 153.0350 151.7650 132.0800 156.2100 140.3350 158.7500
[425] 142.8750 84.4550 151.9428 161.2900 127.9906 160.9852 144.7800 132.0800
[433] 117.9830 160.0200 154.9400 160.9852 165.9890 157.9880 154.9400 97.9932
[441] 64.1350 160.6550 147.3200 146.7000 147.3200 172.9994 158.1150 147.3200
[449] 124.9934 106.0450 165.9890 149.8600 76.2000 161.9250 140.0048 66.6750
[457] 62.8650 163.8300 147.9550 160.0200 154.9400 152.4000 62.2300 146.0500
[465] 151.9936 157.4800 55.8800 60.9600 151.7650 144.7800 118.1100 78.1050
[473] 160.6550 151.1300 121.9200 92.7100 153.6700 147.3200 139.7000 157.4800
[481] 91.4400 154.9400 143.5100 83.1850 158.1150 147.3200 123.8250 88.9000
[489] 160.0200 137.1600 165.1000 154.9400 111.1250 153.6700 145.4150 141.6050
[497] 144.7800 163.8300 161.2900 154.9000 161.3000 170.1800 149.8600 123.8250
[505] 85.0900 160.6550 154.9400 106.0450 126.3650 166.3700 148.2852 124.4600
[513] 89.5350 101.6000 151.7650 148.5900 153.6700 53.9750 146.6850 56.5150
[521] 100.9650 121.9200 81.5848 154.9400 156.2100 132.7150 125.0950 101.6000
[529] 160.6550 146.0500 132.7150 87.6300 156.2100 152.4000 162.5600 114.9350
[537] 67.9450 142.8750 76.8350 145.4150 162.5600 156.2100 71.1200 158.7500
What is the Mean of this dataset? What is its standard deviation?
height weight age male
Min. : 53.98 Min. : 4.252 Min. : 0.00 Min. :0.0000
1st Qu.:125.09 1st Qu.:22.008 1st Qu.:12.00 1st Qu.:0.0000
Median :148.59 Median :40.058 Median :27.00 Median :0.0000
Mean :138.26 Mean :35.611 Mean :29.34 Mean :0.4724
3rd Qu.:157.48 3rd Qu.:47.209 3rd Qu.:43.00 3rd Qu.:1.0000
Max. :179.07 Max. :62.993 Max. :88.00 Max. :1.0000
Call:
lm(formula = height ~ weight, data = howell)
Residuals:
Min 1Q Median 3Q Max
-28.9634 -5.7794 0.7503 6.7207 20.7799
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 75.4359 1.0517 71.72 <2e-16 ***
weight 1.7643 0.0273 64.63 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 9.363 on 542 degrees of freedom
Multiple R-squared: 0.8851, Adjusted R-squared: 0.8849
F-statistic: 4177 on 1 and 542 DF, p-value: < 2.2e-16
Call:
lm(formula = height ~ weight + age + male, data = howell)
Residuals:
Min 1Q Median 3Q Max
-29.011 -5.409 0.730 6.490 19.735
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 75.94238 1.06471 71.327 < 2e-16 ***
weight 1.65634 0.03740 44.289 < 2e-16 ***
age 0.11247 0.02621 4.291 2.11e-05 ***
male 0.07931 0.80942 0.098 0.922
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 9.222 on 540 degrees of freedom
Multiple R-squared: 0.889, Adjusted R-squared: 0.8884
F-statistic: 1441 on 3 and 540 DF, p-value: < 2.2e-16